I would say that for the most part, a statically typed language can do the same things a dynamic language can do, but not the other way around. Another commenter mentions the Any type, but I don't think that's it. It's maps. Rich wants to be able to combine maps with a union operation, take subsets of keys, etc. And that is exactly what maps afford. I'd rather work in a language like Haskell where I can use strong types when I need them and drop down to untyped maps when I need them than a language like Clojure where all I ever have is the maps.
Another thing static types do for you is that they make things in your application more discoverable. Instead of tracing through to figure out which data is available and operations something supports, the compiler tells you. I'd rather work in a language where my compiler can help me this way than in one where it can't.